1 Answer
1

You have three variables, so the "first derivative" is a little ambiguous. You can take a derivative with respect to one of these and feed the solution in directly, e.g.

D[V[a, h, tau], a] /. {a -> 8.47344, h -> 1.67718, tau -> 12.9438}

(Spoiler: none of them are zero)

When you take the total derivative Dt[V[a, h, t], a, h, tau], it gives you a result in terms of the relationship between the variables, such as Dt[a,h] or Dt[h,tau]. You have to specify what these are from you original problem. Substituting in numbers directly gives nonsensical expression such as Dt[8.47344, 1.67718]. You can't take the derivative of a number with respect to a number.

You could also ask Mathematica when one of the first derivatives is zero:

You don't have to calculate the derivatives one by one. To calculate all the first order partial derivatives at the specified point in one go you can do something like D[V[a, h, tau], {{a, h, tau}}] /. {a -> 8.47344, h -> 1.67718, tau -> 12.9438}
–
HeikeMar 20 '12 at 22:09

Mathematica is a registered trademark of Wolfram Research, Inc. While the mark is used herein with the limited permission of Wolfram Research, Stack Exchange and this site disclaim all affiliation therewith.